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An introduction to tile-based self-assembly and a survey of recent results

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Abstract

We first give an introduction to the field of tile-based self-assembly, focusing primarily on theoretical models and their algorithmic nature. We start with a description of Winfree’s abstract Tile Assembly Model (aTAM) and survey a series of results in that model, discussing topics such as the shapes which can be built and the computations which can be performed, among many others. Next, we introduce the more experimentally realistic kinetic Tile Assembly Model (kTAM) and provide an overview of kTAM results, focusing especially on the kTAM’s ability to model errors and several results targeted at preventing and correcting errors. We then describe the 2-Handed Assembly Model (2HAM), which allows entire assemblies to combine with each other in pairs (as opposed to the restriction of single-tile addition in the aTAM and kTAM) and doesn’t require a specified seed. We give overviews of a series of 2HAM results, which tend to make use of geometric techniques not applicable in the aTAM. Finally, we discuss and define a wide array of more recently developed models and discuss their various tradeoffs in comparison to the previous models and to each other.

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Notes

  1. The restriction on overlap is a formalization of the physical mechanism of steric protection.

  2. with the convention that \(\infty = \infty + 1 = \infty - 1\)

  3. Note that a supertile \(\tilde{\alpha}\) could be non-terminal in the sense that there is a producible supertile \(\tilde{\beta}\) such that \(C^\tau_{\tilde{\alpha},\tilde{\beta}} \neq \emptyset,\) yet it may not be possible to produce \(\tilde{\alpha}\) and \(\tilde{\beta}\) simultaneously if some tile types are given finite initial counts, implying that \(\tilde{\alpha}\) cannot be “grown” despite being non-terminal. If the count of each tile type in the initial state is ∞, then all producible supertiles are producible from any state, and the concept of terminal becomes synonymous with “not able to grow”, since it would always be possible to use the abundant supply of tiles to assemble \(\tilde{\beta}\) alongside \(\tilde{\alpha}\) and then attach them.

References

  • Abel Z, Benbernou N, Damian M, Demaine E, Demaine M, Flatland R, Kominers S, Schweller R (2010) Shape replication through self-assembly and RNase enzymes. In: Proceedings of the twenty-first annual ACM-SIAM symposium on discrete algorithms, SODA 2010, Austin, Texas, Society for Industrial and Applied Mathematics

  • Adleman LM (1994) Molecular computation of solutions to combinatorial problems. Science 266(11):1021–1024

    Article  Google Scholar 

  • Adleman L (2000) Toward a mathematical theory of self-assembly (extended abstract), Tech. Report 00-722, University of Southern California

  • Adleman L, Cheng Q, Goel A, Huang M-D (2001) Running time and program size for self-assembled squares. In: Proceedings of the 33rd annual ACM symposium on theory of computing, Hersonissos, Greece, pp 740–748

  • Adleman L, Cheng Q, Goel A, Huang M-D, Wasserman H (2001) Linear self-assemblies: equilibria, entropy and convergence rates. In: Sixth international conference on difference equations and applications, Taylor and Francis

  • Adleman LM, Cheng Q, Goel A, Huang M-D A, Kempe D, de Espanés PM, Rothemund PWK (2002) Combinatorial optimization problems in self-assembly. In: Proceedings of the thirty-fourth annual ACM symposium on theory of computing, pp 23–32

  • Barish RD, Schulman R, Rothemund PWK, Winfree E (2009) An information-bearing seed for nucleating algorithmic self-assembly. Proc Natl Acad Sci USA 106(15):6054–6059

    Article  Google Scholar 

  • Becker F (2009) Pictures worth a thousand tiles, a geometrical programming language for self-assembly. Theor Comput Sci 410(16):1495–1515

    Article  MATH  Google Scholar 

  • Becker F, Rapaport I, Rémila E (2006) Self-assembling classes of shapes with a minimum number of tiles, and in optimal time. In: Arun-Kumar S, Garg N (eds) Foundations of software technology and theoretical computer science (FSTTCS). Lecture notes in computer science, vol 4337, Springer, Berlin, pp 45–56

  • Becker F, Rémila É, Schabanel N (2008) Time optimal self-assembly for 2d and 3d shapes: the case of squares and cubes. In: Ashish G, Simmel FC, and Sosík P, (eds) DNA computing. 14th international meeting on DNA computing, DNA 14, Prague, Czech Republic, June 2–9 2008. Revised Selected Papers. Lecture notes in computer science, vol 5347, Springer, Berlin, pp 144–155

  • Behsaz B, Maňuch J, Ladislav S (2012) Turing universality of step-wise and stage assembly at temperature 1. In: Stefanovic D, Turberfield A (eds) DNA computing and molecular programming. Lecture notes in computer science, vol 7433, Springer, Berlin, pp 1–11

  • Berger R (1965) Undecidability of the domino problem. Memoirs of the American Mathematical Society, Providence, RI

    Google Scholar 

  • Brun Y (2008) Solving np-complete problems in the Tile Assembly Model. Theor Comput Sci 395(1):31–46

    Article  MATH  MathSciNet  Google Scholar 

  • Bryans N, Chiniforooshan E, Doty D, Kari L, Seki S (2011) The power of nondeterminism in self-assembly. In: Proceedings of the 22nd annual ACM-SIAM symposium on discrete algorithms, SODA 2011, SIAM, pp 590–602

  • Cairns-Smith AG (1966) The origin of life and the nature of the primitive gene. J Theor Biol 10(1):53–88

    Article  Google Scholar 

  • Cairns-smith AG (1988) The chemistry of materials for artificial darwinian systems. Int Rev Phys Chem 7(3):209–250

    Article  Google Scholar 

  • Cannon S, Demaine ED, Demaine ML, Eisenstat S, Patitz MJ, Schweller R, Summers SM, Winslow A (2012) Two hands are better than one (up to constant factors). Tech. Report 1201.1650, Computing Research Repository

  • Chandesris J, Dennunzio A, Formenti E, Manzoni L (2011) Computational aspects of asynchronous cellular automata. In: Proceedings of the 15th international conference on developments in language theory, DLT’11, Springer, Berlin, pp 466–468

  • Chandran H, Gopalkrishnan N, Reif JH (2009) The tile complexity of linear assemblies. In: Albers S, Marchetti-Spaccamela A, Matias Y, Nikoletseas SE, and Thomas W (eds) Automata, languages and programming, 36th international colloquium, ICALP 2009, Rhodes, Greece, July 5–12 2009. Proceedings, Part I. Lecture notes in computer science, vol 5555, Springer, Berlin, pp 235–253

  • Chen H-L, Goel A (2004) Error free self-assembly using error prone tiles. In: Proceedings of the 10th international meeting on DNA based computers, pp 274–283

  • Chen H-L, Kao M-Y (2011) Optimizing tile concentrations to minimize errors and time for dna tile self-assembly systems. In: Proceedings of the 16th international conference on DNA computing and molecular programming, DNA’10, Springer, Berlin, pp 13–24

  • Chen H-L, Doty D (2012) Parallelism and time in hierarchical self-assembly. In: Proceedings of the 23rd annual ACM-SIAM symposium on discrete algorithms, SODA 2012, SIAM, pp 1163–1182

  • Chen H-L, Doty D, Seki S (2011) Program size and temperature in self-assembly. In: Proceedings of the 22nd international symposium on algorithms and computation, ISAAC 2011. Lecture notes in computer science, vol 7074, Springer, Berlin, pp 445–453

  • Chen H-L, Goel A, Winfree E, Luhrs C (2007a) Self-assembling tile systems that heal from small fragments. In: Preliminary Proceedings of DNA Computing, vol 30, pp 30–46

  • Chen H-L, Schulman R, Goel A, Winfree E (2007b) Reducing facet nucleation during algorithmic self-assembly. Nano Lett 7(9):2913–2919

    Article  Google Scholar 

  • Cheng Z, Xiao J (2012) Algorithmic tile self-assembly model for the minimum set cover problem. J Bionanosci 6(2):69–77

    Article  MathSciNet  Google Scholar 

  • Cheng Z, Chen Z, Huang Y, Zhang X, Xu J (2010) Implementation of the timetable problem using self-assembly of DNA tiles. Int J Comput Commun Control V(4):490–505

    Google Scholar 

  • Cheng Q, Aggarwal G, Goldwasser MH, Kao M-Y, Schweller RT, de Espanés PMoisset (2005) Complexities for generalized models of self-assembly. SIAM J Comput 34:1493–1515

    Article  MATH  MathSciNet  Google Scholar 

  • Cook M, Fu Y, Schweller RT (2011) Temperature 1 self-assembly: Deterministic assembly in 3D and probabilistic assembly in 2D. In: Proceedings of the 22nd annual ACM-SIAM symposium on discrete algorithms, SODA 2011, SIAM

  • Culik K II (1996) An aperiodic set of 13 Wang tiles. Discret Math160(1–3):245–251

    Article  MATH  MathSciNet  Google Scholar 

  • Czeizler E, Popa A (2012) Synthesizing minimal tile sets for complex patterns in the framework of patterned dna self-assembly. In: Stefanovic D, Turberfield A (eds) DNA Computing and Molecular Programming. Lecture notes in computer science, vol 7433, Springer, Berlin, pp 58–72

  • Demaine ED, Patitz MJ, Schweller RT, Summers SM (2011) Self-assembly of arbitrary shapes using RNAse enzymes: meeting the Kolmogorov bound with small scale factor (extended abstract). Symposium on theoretical aspects of computer science, STACS 2011, pp 201–212

  • Demaine ED, Eisenstat S, Ishaque M, Winslow A (2012) One-dimensional staged self-assembly. Nat Comput 12(2):247–258. English

    Article  MathSciNet  Google Scholar 

  • Demaine ED, Patitz MJ, Rogers TA, Schweller RT, Summers SM, Woods D (2013) The two-handed Tile Assembly Model is not intrinsically universal. In: Proceedings of the fortieth international colloquium on automata, languages and programming, ICALP 2013 (to appear)

  • Demaine ED, Demaine ML, Fekete SP, Ishaque M, Rafalin E, Schweller RT, Souvaine DL (2008) Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues. Nat Comput 7(3): 347–370

    Article  MATH  MathSciNet  Google Scholar 

  • Demaine ED, Demaine ML, Fekete SP, Patitz MJ, Schweller RT, Winslow A, Woods D (2012) One tile to rule them all: Simulating any turing machine, tile assembly system, or tiling system with a single puzzle piece, Tech. Report 1212.4756, Computing Research Repository

  • Doty D (2010) Randomized self-assembly for exact shapes. SIAM J Comput 39(8):3521–3552

    Article  MATH  MathSciNet  Google Scholar 

  • Doty D (2012) Theory of algorithmic self-assembly. Commun ACM 55(12): 78–88

    Article  Google Scholar 

  • Doty D, Patitz MJ (2009) A domain specific language for programming in the Tile Assembly Model. In: Proceedings of the fifteenth international meeting on DNA computing and molecular programming, Fayetteville, Arkansas, USA, June 8–11 2009, pp 25–34

  • Doty D, Patitz MJ, Summers SM (2011) Limitations of self-assembly at temperature 1. Theor Comput Sci 412:145–158

    Article  MATH  MathSciNet  Google Scholar 

  • Doty D, Kari L, Masson B (2013) Negative interactions in irreversible self-assembly. Algorithmica 66(1):153–172

    Article  MATH  MathSciNet  Google Scholar 

  • Doty D, Lutz JH, Patitz MJ, Summers SM, Woods D (2009) Intrinsic universality in self-assembly. In: Proceedings of the 27th international symposium on theoretical aspects of computer science, pp 275–286

  • Doty D, Patitz MJ, Reishus D, Schweller RT, Summers SM (2010) Strong fault-tolerance for self-assembly with fuzzy temperature. In: Proceedings of the 51st annual IEEE symposium on foundations of computer science, FOCS 2010, pp 417–426

  • Doty D, Lutz JH, Patitz MJ, Schweller RT, Summers SM, Woods D (2012) The Tile Assembly Model is intrinsically universal. In: Proceedings of the 53rd annual IEEE symposium on foundations of computer science, FOCS 2012 (to appear)

  • Fu B, Patitz MJ, Schweller RT, Sheline R (2012) Self-assembly with geometric tiles. In: Proceedings of the 39th international colloquium on automata, languages and programming, ICALP (to appear)

  • Fujibayashi K, Zhang DY, Winfree E, Murata S (2009) Error suppression mechanisms for DNA tile self-assembly and their simulation. Nat Comput 8(3):589–612

    Article  MATH  MathSciNet  Google Scholar 

  • Göös M, Orponen P (2010) Synthesizing minimal tile sets for patterned dna self-assembly. In: Sakakibara Y, Mi Y (eds) DNA. Lecture notes in computer science, vol 6518, Springer, Berlin, pp 71–82

  • Hartmanis J, Stearns RE (1965) On the computational complexity of algorithms. Trans Am Math Soc 117:285–306

    Article  MATH  MathSciNet  Google Scholar 

  • Hopfield JJ (1974) Kinetic proofreading: a new mechanism for reducing errors in biosynthetic processes requiring high specificity. Proc Natl Acad Sci USA 71(10):4135–4139

    Article  Google Scholar 

  • Ingerson TE, Buvel RL (1984) Structure in asynchronous cellular automata. Phys D 10(1–2):59–68

    Article  MathSciNet  Google Scholar 

  • Jang B, Kim Y-B, Lombardi F (2006) Error tolerance of DNA self-assembly by monomer concentration control. IEEE international symposium on defect and fault-tolerance in VLSI systems, Arlington, VA, October 4–6, 2006, pp 89–97

  • Jonoska N, McColm GL (2006) Flexible versus rigid tile assembly. In: Calude CS, Dinneen MJ, Pun G, Rozenberg G, and Stepney S (eds) Unconventional computation. Lecture notes in computer science, vol 4135, Springer, Berlin, pp 139–151

  • Jonoska N, McColm GL (2009) Complexity classes for self-assembling flexible tiles. Theor Comput Sci 410(4–5): 332–346

    Article  MATH  MathSciNet  Google Scholar 

  • Jonoska N, Karpenko D (2012) Active tile self-assembly, self-similar structures and recursion. Tech. Report 1211.3085, Computing Research Repository

  • Jonoska N, Karl SA, Saito M (1999) Three dimensional DNA structures in computing. BioSystems 52(1–3):143–153.

    Article  Google Scholar 

  • Kao M-Y, Schweller R (2008) Randomized self-assembly for approximate shapes. In: Proceedings of the 35th international colloquium on automata, languages and programming, Part I, ICALP ’08, Springer, Berlin, pp 370–384

  • Kari L, Seki S, Xu Z (2012) Triangular and hexagonal tile self-assembly systems. In: Proceedings of the 2012 international conference on theoretical computer science: computation, physics and beyond, WTCS’12, Springer, Berlin, pp 357–375

  • Kautz SM, Shutters B (2011) Self-assembling rulers for approximating generalized sierpinski carpets. In: Fu B, Du D-Z (eds) COCOON. Lecture notes in computer science, vol 6842, Springer, Berlin, pp 284–296

  • Lathrop JI, Lutz JH, Summers SM (2009) Strict self-assembly of discrete Sierpinski triangles. Theor Comput Sci 410:384–405

    Article  MATH  MathSciNet  Google Scholar 

  • Lathrop JI, Lutz JH, Patitz MJ, Summers SM (2011) Computability and complexity in self-assembly. Theory Comput Syst 48(3): 617–647

    Article  MATH  MathSciNet  Google Scholar 

  • Lempiäinen T, Czeizler E, Orponen P (2011) Synthesizing small and reliable tile sets for patterned DNA self-assembly. In: Proceedings of the 17th international conference on DNA computing and molecular programming, DNA’11, Springer, Berlin, pp 145–159

  • Luhrs C (2008) Polyomino-safe DNA self-assembly via block replacement. In: DNA computing: DNA14. Lecture notes in computer science, vol 5347, Springer, Berlin, pp 112–126

  • Lutz JH, Shutters B (2012) Approximate self-assembly of the sierpinski triangle. Theory Comput Syst 51(3):372–400

    Article  MATH  MathSciNet  Google Scholar 

  • Ma X, Lombardi F (2008) Synthesis of tile sets for DNA self-assembly. IEEE Trans CAD Integr Circuits Syst 27(5):963–967

    Article  Google Scholar 

  • Majumder U, Labean TH, Reif JH (2007a) Activatable tiles: compact, robust programmable assembly and other applications. In: Garzon M, Yan H (eds) DNA computing: DNA13. Lecture notes for computer science, Springer, Berlin, pp 15–25

  • Majumder U, LaBean TH, Reif JH (2007b) Activatable tiles for compact error-resilient directional assembly. In: 13th international meeting on DNA computing (DNA13), Memphis, Tennessee, June 4–8 2007

  • Mao C, LaBean TH, Relf JH, Seeman NC (2000) Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407(6803):493–496

    Article  Google Scholar 

  • Maňuch J, Stacho L, Stoll C (2009) Step-assembly with a constant number of tile types. In: Proceedings of the 20th international symposium on algorithms and computation, ISAAC ’09, Springer, Berlin, pp 954–963

  • Maňuch J, Stacho L, Stoll C (2010) Two lower bounds for self-assemblies at temperature 1. J Comput Biol 17(6):841–852

    Article  MathSciNet  Google Scholar 

  • Meunier P-E, Patitz MJ, Summers SM, Theyssier G, Winslow A, Woods D (2013) Intrinsic universality in tile self-assembly requires cooperation. Tech. Report 1304.1679, Computing Research Repository

  • Ninio J (1975) Kinetic amplification of enzyme discrimination. Biochimie 57(5):587–595

    Article  Google Scholar 

  • Padilla JE, Liu W, Seeman NC (2012) Hierarchical self assembly of patterns from the robinson tilings: DNA tile design in an enhanced Tile Assembly Model. Nat Comput 11(2):323–338

    Article  MathSciNet  Google Scholar 

  • Padilla JE, Patitz MJ, Pena R, Schweller RT, Seeman NC, Sheline R, Summers SM, Zhong X (2012) Asynchronous signal passing for tile self-assembly: Fuel efficient computation and efficient assembly of shapes. Tech. Report 1202.5012, Computing Research Repository

  • Patitz MJ (2009) Simulation of self-assembly in the abstract Tile Assembly Model with ISU TAS. In: 6th annual conference on foundations of nanoscience: self-assembled architectures and devices, Snowbird, Utah, USA, April 20–24 2009

  • Patitz MJ (2012) An introduction to tile-based self-assembly. In: Durand-Lose J, Jonoska N (eds) Unconventional computation and natural computation. Lecture notes in computer science, vol 7445, Springer, Berlin, pp 34–62

  • Patitz MJ, Summers SM (2010) Self-assembly of discrete self-similar fractals. Nat Comput 1:135–172

    Article  MathSciNet  Google Scholar 

  • Patitz MJ, Summers SM (2011) Self-assembly of decidable sets. Nat Comput 10(2): 853–877

    Article  MATH  MathSciNet  Google Scholar 

  • Patitz MJ, Summers SM (2012) Identifying shapes using self-assembly. Algorithmica 64(3):481–510

    Article  MATH  MathSciNet  Google Scholar 

  • Patitz MJ, Schweller RT, Summers SM (2011) Exact shapes and turing universality at temperature 1 with a single negative glue. In: Proceedings of the 17th international conference on DNA computing and molecular programming, DNA’11, Springer, Berlin, pp 175–189

  • Patitz MJ, Schweller RT, Summers SM (2012) Efficient squares and turing universality at temperature 1 with a unique negative glue. Tech. Report 1105.1215v2, Computing Research Repository

  • Penrose R (1979) Set of tiles for covering a surface. US Patent 4133152

  • Reif JH (1999) Local parallel biomolecular computing. In: Proceedings of DNA Based Computers III, DIMACS, American Mathematical Society, Providence, RI, vol 48, pp 217–254

  • Reif J, Sahu S, Yin P (2006) Complexity of graph self-assembly in accretive systems and self-destructible systems. In: Carbone A, Pierce N (eds) DNA computing. Lecture notes in computer science, vol 3892, Springer, Berlin, pp 257–274

  • Rothemund PWK (2001) Theory and experiments in algorithmic self-assembly. Ph.D. thesis, University of Southern California

  • Rothemund PWK (2006) Folding DNA to create nanoscale shapes and patterns. Nature 440(7082): 297–302

    Article  Google Scholar 

  • Rothemund PWK, Winfree E (2000) The program-size complexity of self-assembled squares (extended abstract). In: Proceedings of the thirty-second annual ACM symposium on theory of computing, STOC ’00, Portland, Oregon, United States, ACM, pp 459–468

  • Rothemund PWK, Papadakis N, Winfree E (2004) Algorithmic self-assembly of DNA sierpinski triangles. PLoS Biol 2(12): e424

    Article  Google Scholar 

  • Schulman R, Winfree E (2009) Programmable control of nucleation for algorithmic self-assembly. SIAM J Comput 39(4): 1581–1616

    Article  MATH  MathSciNet  Google Scholar 

  • Schulman R, Winfree E (2011) Simple evolution of complex crystal species. In: Proceedings of the 16th international conference on DNA computing and molecular programming, DNA’10, Springer, Berlin, pp 147–161

  • Schulman R, Yurke B, Winfree E (2012) Robust self-replication of combinatorial information via crystal growth and scission. Proc Natl Acad Sci USA 109(17):6405–10

    Article  Google Scholar 

  • Schweller RT, Sherman M (2013) Fuel efficient computation in passive self-assembly. In: Proceedings of the 24rd annual ACM-SIAM symposium on discrete algorithms, SODA 2013, SIAM, pp 1513–1525

  • Seeman NC (1982) Nucleic-acid junctions and lattices. J Theor Biol 99:237–247

    Article  Google Scholar 

  • Seki S, Okuno Y (2012) On the behavior of tile assembly system at high temperatures. In: Barry Cooper S, Dawar A, and Löwe B (eds) How the world computes. Proceedings of the Turing centenary conference, CiE 2012, Cambridge, United Kingdom, June 18–23, 2012. Lecture notes in computer science, vol 7318, Springer, Berlin, pp 550–560 (Eng)

  • Seki S (2013) Combinatorial optimization in pattern assembly. Tech. Report 1301.3771, Computing Research Repository

  • Soloveichik D, Winfree E (2005) Complexity of compact proofreading for self-assembled patterns. In: Carbone A, Pierce NA (eds) DNA computing. The eleventh international meeting on DNA computing. Lecture notes in computer science, vol 3892, Springer, Berlin, pp 305–324

  • Soloveichik D, Winfree E (2007) Complexity of self-assembled shapes. SIAM J Comput 36(6):1544–1569

    Article  MATH  MathSciNet  Google Scholar 

  • Soloveichik D, Cook M, Winfree E (2008) Combining self-healing and proofreading in self-assembly. Nat Comput 7(2):203–218

    Article  MathSciNet  Google Scholar 

  • Summers SM (2012) Reducing tile complexity for the self-assembly of scaled shapes through temperature programming. Algorithmica 63(1–2):117–136

    Article  MATH  MathSciNet  Google Scholar 

  • Wang H (1961) Proving theorems by pattern recognition—II. Bell Syst Tech J XL(1):1–41

    Article  Google Scholar 

  • Wang H (1963) Dominoes and the AEA case of the decision problem. In: Proceedings of the symposium on mathematical theory of automata, New York, 1962, Polytechnic Press of Polytechnic Inst. of Brooklyn, Brooklyn, pp 23–55

  • Wang Y, Lu W, Bai X, Wei D, Cui G (2011) DNA tile assembly for degree-constrained minimum spanning tree. J Bionanosci 5(1):41–46

    Article  Google Scholar 

  • Winfree E The xgrow simulator. http://www.dna.caltech.edu/Xgrow. Accessed 17 June 2013

  • Winfree E (1998) Algorithmic self-assembly of DNA. Ph.D. thesis, California Institute of Technology

  • Winfree E (2006) Self-healing tile sets. In: Chen J, Jonoska N, and Rozenberg G (eds) Nanotechnology: science and computation. Natural computing series, Springer, Berlin, pp 55–78

  • Winfree E, Bekbolatov R (2003) Proofreading tile sets: Error correction for algorithmic self-assembly. In: Chen J, Reif JH (eds) DNA computing. Lecture notes in computer science, vol 2943, Springer, Berlin, pp 126–144

  • Winfree E, Liu F, Wenzler LA, Seeman NC (1998) Design and self-assembly of two-dimensional DNA crystals. Nature 394(6693):539–44

    Article  Google Scholar 

  • Woo S, Rothemund PWK (2011) Programmable molecular recognition based on the geometry of DNA nanostructures. Nat Chem 3(8): 620–7

    Article  Google Scholar 

  • Woods D, Chen H-L, Goodfriend S, Dabby N, Winfree E, Yin P (2013) Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In: Proceedings of the 4th conference on innovations in theoretical computer science, ITCS ’13, New York, NY, USA, ACM, pp 353–354

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Acknowledgments

The author would like to thank Scott Summers, Damien Woods, and Dave Doty for much helpful guidance and advice in putting together this survey. He would also like thank Nataša Jonoska and Jérôme Durand-Lose for the invitation to write it. Finally, he is greatly indebted to two anonymous reviewers whose extremely thorough reviews and comments greatly improved this manuscript. This author’s research was supported in part by National Science Foundation Grant CCF-1117672.

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    Matthew J. Patitz

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Patitz, M.J. An introduction to tile-based self-assembly and a survey of recent results. Nat Comput 13, 195–224 (2014). https://doi.org/10.1007/s11047-013-9379-4

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